Overview: The "15-puzzle" is a
common children's toy. It consists of a square container. In this
container, are placed 15 smaller square blocks. The length of each block
is about 1/4th the length of the container. So, the container can
accommodate 4 rows of 4 blocks each (16 blocks in all).

The game comes with 15 blocks. These are numbered
1,2,3...and so on. The 16th place is left free. It looks something
like this:

The objective is to slide the blocks, one at a time
until one has all the blocks organized in some fashion. For instance, a
common goal is to try to organize the blocks so that the numbers are in
ascending order, row by row, top to bottom.

The Goal:.

How would one get from the "shuffled" state
to the goal state?

Playing: Look at the shuffled state in the picture to the left.
There are three possible moves:

Move the "5" down; or,

Move the "3" to the left; or,

Move the "13" up

One might move the "5" down, then one might
move the "1" to the left, so that it occupies top-left
position, where you want it to be. Then, similarly, one might move the
"2" to its final position, and so on.